Related papers: First-order linear evolution equations with c\`adl…
We present a general method of solving the Cauchy problem for multidimensional parabolic (diffusion type) equation with variable coefficients which depend on spatial variable but do not change over time. We assume the existence of the…
In this paper we study the following non-autonomous stochastic evolution equation on a UMD Banach space $E$ with type 2, {equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), \quad t\in [0,T],…
Quasilinear (and semilinear) parabolic problems of the form $v'=A(v)v+f(v)$ with strict inclusion $\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function $v\mapsto f(v)$ and the quasilinear part $v\mapsto A(v)$ are…
In this paper, we deal with the existence of $\omega$-periodic mild solutions for the abstract evolution equation with delay in an ordered Banach space $E$ $$u'(t)+Au(t)=F(t,u(t),u(t-\tau)),\ \ \ \ t\in\R,$$ where $A:D(A)\subset…
We study parabolic stochastic partial differential equations (SPDEs), driven by two types of operators: one linear closed operator generating a $C_0-$semigroup and one linear bounded operator with Wick-type multiplication, all of them set…
In this paper, we announce a rigorous approach to establishing uniqueness results, under certain conditions, for initial-boundary-value problems for a class of linear evolution partial differential equations (PDEs) formulated in a…
We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial condition, written in general form which includes, as…
We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the underlying PDE, we seek to approximate the evolution operator of…
We study the Cauchy problem for the focusing nonlinear Schrodinger (NLS) equation. Using the DBAR generalization of the nonlinear steepest descent method we compute the long time asymptotic expansion of the solution in any fixed space-time…
We present first results on the Dirichlet-to-Neumann operator associated with the $1$-Laplace operator in $L^1$. In particular, we show that this operator can be realized as a sub-differential operator in $L^1\times L^{\infty}$ of a…
We consider a family of linear singularly perturbed PDE relying on a complex perturbation parameter $\epsilon$. As in a former study of the authors (A. Lastra, S. Malek, Parametric Gevrey asymptotics for some nonlinear initial value Cauchy…
This paper develops the necessary ingredients for the variational approach of initial boundary-value problems of parabolic partial differential equations on a fixed spatial domain containing evolving subdomains. In particular, we introduce…
We study linear stochastic partial differential equations of parabolic type. We consider a new boundary value problem where a Cauchy condition is replaced by a prescribed average of the solution either over time and probabilistic space for…
For an arbitrary parameter $p\in [1,+\infty]$, we consider the problem of exponential stabilization in the spatial $L^{p}$-norm, and $W^{1,p}$-norm, respectively, for a class of anti-stable linear parabolic PDEs with space-time-varying…
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…
We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over R^d and in L^p-spaces with respect to tight evolution systems of measures. Here, the linear part…
We present the numerical solution of two-point boundary value problems for a third order linear PDE, representing a linear evolution in one space dimension. The difficulty of this problem is in the numerical imposition of the boundary…
We study inverse boundary problems for evolutionary PDEs using only a single passive boundary observation, where data from an unknown internal source propagate through an unknown medium without active inputs. The goal is the simultaneous…
While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…